Computer Methods for Determination of Deformations in Welded Closed Profiles

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ScienceDirect Procedia Engineering 177 (2017) 188 – 195

XXI International Polish-Slovak Conference “Machine Modeling and Simulations 2016”

Computer methods for determination of deformations in welded closed profiles Zbigniew Saternus Institute of Mechanics and Machine Design Foundations, Częstochowa University of Technology, Dabrowskiego 73, Częstochowa, Poland

Abstract The work concerns the numerical prediction of deformations in welding of two rectangular profiles using TIG method. Numerical analysis of thermomechanical phenomena are carried out in the Abaqus FEA software using finite element method. Geometry of the joint is numerically recreated on the basis of the real welded joint of rectangular profiles. For this geometry a discretization of the system and numerical simulations of welding deformations are performed. The calculations are performed for the rectangular profiles made of steel X5CrNi18-10. Numerical analysis takes into account thermomechanical properties of welded elements changing with temperature. DFLUX subroutine is used in Abaqus software, allowing the modeling of moveable welding heat source. Mathematical Goldak`s description of the heat source is assumed to described the distribution of movable heat source power. Results of numerical analysis of the temperature distribution in the welded joint are presented in this study. The estimation of the shape and size of melted zone is performed as well as the prediction of stress state and welding deformations. Numerically predicted deformations are compared with results of the measurement. © 2017 Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license 2017The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016. Peer-review under responsibility of the organizing committee of MMS 2016 Keywords: GTAW welding; numerical analysis; displacement; stainless steel; closed profile;

1. Introduction Different metal joining methods are currently used in the manufacturing industry [1-3]. Arc methods are still used in spite of advanced joining technologies. This results from the significantly lower costs of production and the cost of welding equipment [4, 5]. For every welding technology, an important issue is the determination of welding stress and strain generated in the weld and adjacent area [3, 5]. The prediction of strain location at an early stage of design of welded constructions allow to change process parameters in order to reduce deformations in the joint [4]. This significantly improves the quality and mechanical properties of the final product [6, 7]. Due to the high costs of conducting experimental research, more often numerical analysis is performed on the basis of finite element method [8-11].

Corresponding author. Tel.:+48 34 325 06 49; fax: ++48 34 325 06 47. E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016

doi:10.1016/j.proeng.2017.02.219

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Zbigniew Saternus / Procedia Engineering 177 (2017) 188 – 195

Numerical analysis of thermomechanical phenomena in TIG welding process of two orthogonally arranged closed rectangular profiles is performed in this paper. A three-dimensional discrete model of considered system is created in Abaqus/FEA software. The geometry of analyzed model corresponds to the geometry of a real object. Thermo-mechanical properties varying on temperature are assumed in calculations for welded profiles made of X5CrNi18-10 stainless steel [3]. Abaqus/Standard module is used in calculations where additional subroutine DFLUX is implemented. The mathematical model of moveable heat source power distribution is implemented and its location relative to connected parts. Temperature field is determined on the basis of numerical simulations of welded joints [12]. The size and shape of melted zone as well as welding deformations are numerically estimated. Values of predicted displacements are compared to measurements made on the real joint. 2. Analysis of thermomechanical phenomana in Abaqus/FEA Numerical analysis of temperature field in electric arc welded joints (TIG) is determined on the basis of the solution of energy conservation equation with Fourier law [13]. Temperature field is expressed as follows:

³U V

wU wGT GT dV  wt wxD V

³

§ wT ˜ ¨¨ O © wxD

· ¸¸dV ¹

³ GT q dV  ³ GT q dS V

V

S

(1)

S

where O is a thermal conductivity [W/m °C], U = U(T) is a internal energy [J/kg], qv is a laser beam heat source [W/m3], T = T(xD,t) is a temperature [°C], qs is a boundary heat flux [W/m2], GT is a variational function, U is a density [kg/m3], T = T(xα,t) is temperature [°C]. Equation (1) is completed by initial condition t = 0 : T = To and boundary conditions of Dirichlet, Neumann and Newton type with the heat loss due to convection and radiation. Solid - liquid phase transformation is taken into account in the mathematical model of thermal phenomena [14, 15], assuming solidus temperature TS=1400 [°C], liquidus TL=1455 [°C] and latent heat of fusion HL=260u103 [J/kg]. The mechanical analysis in elastic-plastic range is based on classic equilibrium equations, supplemented by constitutive relations [3, 5, 6]. Equation (1) is completed by initial and boundary conditions.

’ $ σ xD , t 0,

σ

σ σ T

(2)

 $ εe D $ ε e  D

σxD , t0 σxD , TS 0,

(3)

ε e xD , t0 ε e xD , TS 0

(4)

where σ=σ(σij) is stress tensor, xα describes location of considered point (material particle), ( $ ) is inner exhaustive product, D=D(T) is a tensor of temperature dependent material properties. The total strain is defined as a sum of elastic εe, plastic εp and thermal εTh strains:

H total

H e  H p  H Th

(5)

Elastic strain is modelled using an isotropic Hooke's law, whereas plastic strain is calculated using plastic flow model obeying Huber-Misses plasticity condition [6].

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3. Movable heat source model The distribution of the intensity of electric arc power in the literature on numerical analysis of TIG welding method is often described using Goldak’s model. [16]. Mathematical model of Goldak’s heat source is described by two half ellipsoids connected together by a symmetry axis. The model is defined in set of two equations:

Q1 ( x, y, z ) Q2 ( x, y, z )

6 3 f1QA abc1S S 6 3 f 2 QA abc2S S

exp( 3

x2 y2 z2 ) exp( 3 2 ) exp( 3 2 ) 2 a b c1

exp( 3

x2 y2 z2 ) exp( 3 2 ) exp( 3 2 ) 2 a b c2

(6)

where a, b, c1 and c2 are dimensions of semi-ellipsoid axes, coefficients f1 and f2 (f1 + f2 = 2) are representing energy distribution in the front and in the back of the heat source, satisfying the condition Q1(x,y,z) and Q2(x,y,z). In this equation, the power of the electric arc QA=ηIU is determined by the process parameters: voltage U [V] and current intensity I [A] as well as the efficiency η. Scheme of considered numerical models and exemplary Goldak’s heat source power distribution are shown in Fig. 1.

Fig. 1. Goldak heat source: a) scheme, b) exemplary heat source power distribution.

Welding heat source model is implemented into solver using additional DFLUX subroutine written in FORTRAN programming language [3, 5, 13]. Coordinates of the centre of welding heat source are determined for each time step, depending on the assumed welding speed (analysis is performed in Lagrange coordinates). In order to adopt the correct positioning of Goldak`s heat source regard to joined elements the transformation of power distribution of heat source is carried out. The basic system is rotated by a given angle using transformation equations:

Aic

J icj Aj

where

J icj

e˜ e c i

j

(7)

On the basis of general transformation equations (7) equations of transition form the primary system to rotated system by a given angle D are obtained:

­x ° ®y °z ¯

xo cos D ˜ y1  sinD ˜ z1  sinD ˜ y1  cos D ˜ z1

(8)

Zbigniew Saternus / Procedia Engineering 177 (2017) 188 – 195

4. Experiment In order to verify the adapted numerical models welding experiment is performed. Figure 2 presented two closed rectangular profiles with dimensions 20x30x2 mm made of stainless steel X5CrNi18-10 joined by TIG method. Single side fillet weld is performed in the experiment. Welding process is performed without additional material, using argon as a shielding gas from the face of the weld. The following process parameters are assumed in the experiment: current I=80 A, voltage U=24 V, speed of the torch v=0.45÷0.6 m/min (literature date for manual welding) and shielding gas flow rate 10 l/min.

Fig. 2. Experimentally obtained welded joint made of closed profiles.

Displacements are measured in experimentally obtained welded joint made of closed profiles. Measurements of the angles before and after welding are made in order to determinate the values of displacements of ends of profiles (Fig. 3a-3c). Then, values of displacement are determined on the basis of measured angles, as presented in Fig. 3d.

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Fig. 3. Measurement and analysis of displacement in the welded joint a) angle measurement before welding b) and c) after welding, d) determination of displacement of welded elements.

5. Numerical modeling of TIG welding processes in Abaqus FEA Numerical simulations are performed for welding process of two orthogonally arranged closed rectangular profiles using TIG method. Three-dimensional discrete model of analyzed system is created in Abaqus FEA with real dimensions used in the experiment. Figure 4 presents scheme of considered system and adapted finite element mesh. Temperature dependant thermomechanical properties of welded profiles made of austenitic steel X5CrNi1810 are assumed in calculations according to [3].

Fig. 4. Scheme of considered system and discretization of analyzed domain.

Numerical simulation of thermal and mechanical phenomena in Abaqus FEA is performed in two stages. At first stage numerical calculations of temperature field is performed. A simulation of mechanical phenomena is made at the next stage of calculations using results from thermal analysis. In both thermal and mechanical analysis identical rectangular mesh is used but different types of elements, depending of the type of analysis [7]. The total number of

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elements used in the numerical model is 135056. Boundary conditions assumed in calculations are chosen to provide a static determination of considered system. 6. Results and discussion Goldak's heat source parameters are determined on the basis of experimental data. Heat source power QA is determined by multiplying the voltage and the current and efficiency of the welding process. In the case of manual welding, efficiency of TIG welding and welding speed are adapted according to the literature data: η=45% and v = 0.5 m/min. The shape of the Goldak's heat source is assumed on the basis of model verification: c1= 4mm, c2=8 mm, a=0.8 mm, b=4 mm. The angle of the welding source should be also taken into account in the calculation, as: D O. Figure 5 shows numerically obtained temperature distribution in welded closed profiles, where solid line determines the melted zone boundary (liquidus temperature TL≈ 1455 °C).

Fig. 5. Numerically estimated temperature field in TIG welded joint (a) and in the cross section of welded joint (b).

Figure 5b shows the temperature distribution in the cross section of welded joint where numerically estimated weld shape is pointed out by a solid line.

Fig. 6. von Misses stress distribution for different times.

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Stress state and deformations in the analyzed welded joint were calculated on the basis of numerically estimated temperature field. Figure 6 shows the stress distribution for different times of welding process. The maximum value of the stress equals about 250 MPa. Displacement field is shown in isometric (Fig, 7a) and in YZ plane (Fig. 7b) in order to illustrate the direction of resulting deformations obtained by the simulation. The comparison of calculated directions of displacements at ends of the profile with results of the measurement shows a good consistency of results. In the case of a numerical model of the maximum displacement is approximately 14.5 mm, which in comparison to real joint is a little higher value (in the experiment the value is about 12 mm).

Fig. 7. Numerically estimated deflection UZ in welded closed profiles.

7. Conclusion Developed three-dimensional discrete model in Abaqus FEA software on the basis of the real joint allowed to perform a complete analysis of thermomechanical phenomena in TIG welding process. Numerical simulations with experimental verification allowed the assessment the correctness of developed models for welding process. Comprehensive discrete model made in Abaqus FEA allows to perform analysis of the welding process for any components positioned relative to each other. In this paper temperature field as well as stress and strain fields are determined for two closed profiles welded by TIG method. The maximum value of stress in the analyzed system is approximately 240 MPa (Fig. 6) and significantly decreases with the distance from the welding line. The comparison of numerically estimated displacements of welded profiles with measurements shows fairly good compatibility of results (Fig. 3d and Fig. 7). Resulting directions of displacement are identical and their values are comparable. References [1] [2] [3] [4] [5] [6]

K. Adamus, Z. Kucharczyk, K. Wojsyk, K. Kudla, Numerical analysis of electron beam welding of different grade titanium sheets, Computational Materials Science 77, (2013) 286-294. M. Kubiak, W. Piekarska, S. Stano, Modelling of Laser Beam Heat Source Based on Experimental Research of Yb:YAG Laser Power Distribution, International Journal of Heat and Mass Transfer, 83 (2015) 679-689. Z. Saternus, W. Piekarska, M. Kubiak, T. Domański, L. Sowa, Numerical analysis of deformations in sheets made of X5CRNI18-10 steel welded by a hybrid laser-arc heat source, Procedia Engineering, 136 (2016) 95 – 100. D. Deng, H. Murakawa, Prediction of welding distortion and residual stress in a thin plate butt-welded joint, Computational Materials Science, 43, 2, 2008 353-365. H. Long, D. Gery, A. Carlier, P.G. Maropoulos, Prediction of welding distortion in butt joint of thin plates, Mater Design, 30, (2009) 4126– 4135. T. Domanski, W. Piekarska, M. Kubiak, Z. Saternus, Determination of the final microstructure during processing carbon steel hardening, Procedia Engineering, 136 (2016) 77-81.

Zbigniew Saternus / Procedia Engineering 177 (2017) 188 – 195 [7] [8]

[9] [10] [11] [12] [13] [14] [15] [16]

J. Rojek, M. Hyrcza-Michalska, A. Bokota, W. Piekarska, Determination of Mechanical Properties of the Weld Zone in Tailor-Welded Blanks, ACME, 12, 1 (2012) 56-162. M. Sága, R. Bednár, M. Vaško, 2011 Contribution to Modal and Spectral Interval Finite Element Analysis. In Vibration Problems ICOVP 2011, The 10th International Conference on Vibration Problems: Liberec, Czech Republic. Springer Science+Business Media B. V., (2011) 269–274. A. Sapietová, V. Dekýš, M. Sapieta, P. Pecháč, 2014. Application of computational and design approaches to improve carrier stability. In: Procedia Engineering, 96 (2014) 410-418. J. Zapoměl, V. Dekýš, P. Ferfecki, A. Sapietová, M. Sága, M. Žmindák, 2015. Identification of Material Damping of a Carbon Composite Bar and Study of Its Effect on Attenuation of Its Transient Lateral Vibrations. In International Journal of Applied Mechanics, 7, 6 (2015). P. Kopas, L. Jakubovičová, M. Vaško, M. Handrik, 2016. Fatigue Resistance of Reinforcing Steel Bars. In Procedia Engineering, 136 (2016) 193–197. A. Anca, A. Cardona, J. Risso, et al.; Finite element modeling of welding processes, Appl Math Model, 35, (2011) 688–707. SIMULIA Dassault System, Abaqus theory manual, Version 6.7, 2007. T. Skrzypczak, E. Węgrzyn-Skrzypczak, J. Winczek, Effect of Natural Convection on Directional Solidification of Pure Metal, ARCHIVES OF METALLURGY AND MATERIALS, 60(2) (2015) 835-841. L. Sowa, Effect of steel flow control devices on flow and temperature field in the tundish of continuous casting machine. Archives of Metallurgy and Materials, 60, 2A (2015) 843-847. J. A. Goldak, Computational Welding Mechanics. Springer, New York, 2005.

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